Basic Course in Mathematics ALaajuus (5 ECTS)

Objective

The student knows the basic methods of simplification and solving equations. The student knows the most important applications of exponential and logarithmic function in his/hers field. The student recognizes the plots of the most common functions in bio- and food-engineering. The student is aware of different methods of solving systems of linear equations. The student knows how to apply vectors, straight lines and planes.
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The student is able to visualize with pen and paper the most common functions in in bio- and food-engineering. The student is able to simplify mathematical expressions and to solve simple equations and systems of equations. The student is able to use vectors in various applications, e.g. in physics. The student can plot functions, solve equations and systems of equations using Excel or Matlab.

Content

Simplifying mathematical expressions and solving typical equations in engineering sciences. Plotting functions and simple transformations of them. Applications of exponential and logarithmic functions in microbiology and solving such equations. Solving systems of linear equations and elementary matrix algebra. Applications of systems of linear equations and matrix. algebra in chemistry, life-sciences and physics.

Plane vectors and their applications, e.g. in geometrical and physical problems. Space vectors and their applications, straight line and plane in 3-dimensional spaces and their applications in bio- and food-engineering.

The concept of a function, composite function and inverse function. Examples of functions and plots of functions that are common in bio- and food-engineering.

Using Excel in plotting functions and in solving equations and systems of equations.
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Overdetermined and underdermined systems of linear equations and their applications stoichiometry and food-engineering. Introduction to linear programming. Multidimensional vectors and their interpretations in bio- and food-engineering. Mathematical software (e.g. Matlab, Maple, Maxima, Octave).

Qualifications

Secondary school (ninth grade) mathematics

Further information

Class room teaching: 56 h
Computer labs: 14 h
Exams: 5h
Student individual workload (workload analysis not carried out): 58 h
Total: 133 h
Follow-up of the student workload analysis performed: -